You are not required to sign into an outside account to access basic features of the website and mobile apps, e.g. movie details and showtimes. If you want to use additional features, though, you must log in.
To log in on Flixster.com, click on "Login" at the upper right on any page. If you do not have an account, click on "Sign Up" at the upper right.
To log in on iOS and Android devices, go to the My Movies tab and sign into your existing account. If you have never created an account, you can do so by logging in via Facebook on the My Movies tab, or by going to www.flixster.com (click on "Sign Up" at the upper right).